Graphing Linear Equations

Every linear equation in the form $y = mx + b$ has a secret 'home base.' This is the y-intercept, represented by the letter $b$. The y-intercept is the exact point where your line crosses the vertical y-axis. Because this point sits directly on the y-axis, its $x$-coordinate is always $0$. Therefore, the coordinates for this starting point are always $(0, b)$. Before you can draw your line, you must first 'drop the anchor' at this location on your coordinate plane.

Now that you have a starting point, you need to know which direction to move. The slope ($m$) acts as your directional guide. We describe slope as $\\frac{\text{rise}}{\text{run}}$. The top number (rise) tells you how many units to move up or down, and the bottom number (run) tells you how many units to move right. If the slope is a whole number like $3$, treat it as a fraction: $\\frac{3}{1}$. This means you rise $3$ and run $1$.

Sometimes equations look a bit 'thin' because they are missing a variable. These are special cases. If an equation is $y = c$ (where $c$ is a number), the y-value is always the same, no matter what $x$ is. This creates a horizontal line. If the equation is $x = c$, the x-value is locked, creating a vertical line. A horizontal line has a slope of $0$, while a vertical line has an undefined slope because you cannot 'run' anywhere!